SOLUTION: The profit function for a computer company is given by P(x) = -x^2+ 25x - 24 where x is the number of units produced (in thousands) and the profit is in thousand of dollars. a) De

Question 204208: The profit function for a computer company is given by P(x) = -x^2+ 25x - 24 where x is the number of units produced (in thousands) and the profit is in thousand of dollars.
a) Determine how many (thousands of) units must be produced to yield maximum profit. Determine the maximum profit.
(thousands of) units =?
maximum profit = ? thousand dollars
b) Determine how many units should be produced for a profit of at least 40 thousand.
more than ?(thousands of) units
less than ?(thousands of) units

(the question marks are where I need answers)

Answer by stanbon(48554) (Show Source):
You can put this solution on YOUR website!
The profit function for a computer company is given by P(x) = -x^2+ 25x - 24 where x is the number of units produced (in thousands) and the profit is in thousand of dollars.
a) Determine how many (thousands of) units must be produced to yield maximum profit. Determine the maximum profit.
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Maximum profit occurs when x = -b/2a = -25/(2*-1) = 12.5

(thousands of) units =12.5
maximum profit = -12.5^2+25*12.5 - 24 = 132.5 thousand dollars
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b) Determine how many units should be produced for a profit of at least 40 thousand.
-x^2+25x - 24 >= 40
-x^2+25x-64 = 0
x = [-25 +- sqrt(625 - 4*-1*-64)]/(-2)
x = [-25 +- sqrt(369)]/-2
x = [-25 +- 19.209]/-2
x = 22.1 or x = 2.89
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more than 2.89(thousands of) units
less than 22.1(thousands of) units
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Cheers,
Stan H.